Universal tests for memory words

Gusztav Morvai, Benjamin Weiss

Research output: Contribution to journalArticle

1 Citation (Scopus)


The main result is a universal pointwise test that, when presented with a set of words $S$ on a finite or countable alphabet ${\cal X}$ that purports to be a set of memory words for a stationary process, will eventually almost surely return the value YES precisely when all positive probability words in $S$ are memory words. For example, if $S$ consists of all of the single letters in ${\cal X}$, then the test will eventually say yes if and only if the process is a Markov chain. Various further positive and negative results of this type are also given.

Original languageEnglish
Article number6532389
Pages (from-to)6873-6879
Number of pages7
JournalIEEE Transactions on Information Theory
Issue number10
Publication statusPublished - Sep 25 2013


  • Statistical learning
  • stationary processes
  • stochastic processes

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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